Persistence of Lower Dimensional Hyperbolic Invariant Tori for Nearly Integrable Symplectic Mappings

• Qiaoyan Bi ; Junxiang Xu ^[1]
  1. [1] Southeast University

     Southeast University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 13, Nº 2, 2014, págs. 269-288
• Idioma: inglés
• DOI: 10.1007/s12346-014-0117-9
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• Resumen

  • In this paper we consider a class of nearly integrable symplectic mappings with generating function and prove the persistence of lower dimensional hyperbolic invariant tori. Under a Rüssmann-type non-degenerate condition, by using the KAM theory, we proved that the nearly integrable twist symplectic mappings admit a family of lower dimensional invariant tori as long as the generating function is real analytic and the perturbation is sufficiently small.